> What our > students are most often trained to do (pun intended) is to recognize a > problem as one of a class and recall the technique for its solution, > rather than follow the math as defined in the problem itself wherever it > leads. THAT is what makes them difficult, not whether the student ever > heard the word "hyperbola" before. The graph could have been called a > "sausage" for all it matters, defined as y=a/x.

I agree. You don't see that approach in a typical class. I took algebra 2 in 8th and the class was designed for 8th graders taking algebra 2. The teacher made sure we competed in the math tournaments as well, some of us at least. It is a whole different experience. I see some schools trying to get back into the swing of having advanced classes again.